Baking Normals produces grid mesh on result
You definitely shouldn't need subdivisions to get non grid bakes. Subdivisions can help with extreme gradients, though. 

My guess is that you have the low polygons normals incorrectly prepped for the bake. When you bake details from high poly to low the low poly models normals affect how the rays are cast. 
Make sure that your lowpoly mesh object is set to "smooth" from the: 
3D View-T panel-Tools-Edit-Shading-Smooth 
before exporting. In my tests if you set your low poly to Smooth the bakes come out without the lowpoly edges showing up in the texture. If you set it to Flat the bake comes out with the lines. 

Sometimes you will need to control smoothness/Sharpness at the low poly level, though. In this case first the the object to smooth shading. Then enable auto-smooth in:
Properties panel-Object Data-Normals
and set the value to 180. (Or whatever value you want to use as sharpness. At 180 whole model will be treated as smooth shaded, because 180° doesn't really ever exist in normal model.) Then you can in edit mode set the edges you want as "sharp" by selecting those edges, ctrl-E, mark sharp. This is useful with hardsurface/mechanical stuff. (However, note that the Normals-Autosmooth is very resource intensive when polycount rises so definitely disable it when working with subdivision surfaces.) 

I hope the smooth shading before exporting lowpoly fixes your problem!